Isoparametric foliations on complex projective spaces (Q2796519)

Given an irreducible inner compact symmetric space \(G/K\) of rank greater than one, the authors determine the number \(F({\mathcal F}_{G/K})\) of congruence classes of isoparametric foliations on \({\mathbb C}P^n\) whose pullback via the Hopf map \(S^{2n+1}\to {\mathbb C}P^n\) gives a foliation congruent to \({\mathcal F}_{G/K|}\), the orbit foliation of the isotropy representation of \(G/K\) restricted to the unit sphere of the tangent space \(T_{eK} G/K\). They do the same for some FKM foliations of \(S^{2n+1}\), that is for foliations constructed in [\textit{D. Ferus} et al., Math. Z. 177, 479--502 (1981; Zbl 0443.53037)].